We are used to looking at quadratic equations where "y" is the variable that is equal to the squared "x" terms. However, in a horizontal parabola the "x" is equal to the "y" term squared. Instead of going up and down, a horizontal parabola goes from side to side. When graphing a horizontal parabola, we first need to make sure the formula is in standard form and then plot accordingly.

We are used to looking at quadratic equationsthat are Y is equal to something squared.Okay.

But that doesn't alwayshave to be the case.We could end up dealing with X isequal to something Y squared.And what that really does is take a parabola,which we are used to looking atas up and down, so either straight, coefficientof positive A or negative A. And what it does instead ismake it a sideways problem.So you're dealing with something likethis or something like this.Okay.

Trick is that this isn'tactually a function.Remember that in order to have a functionwe have to have one Y for every X.So if you look at something likethis, that's not going to hold.So this isn't a function, but that doesn'tmean we can't still try to graphit.

So what we can do is in order to graph it,think about what the relating equationis for Y equals.So I have right here X is equal to Yplus 1 squared minus 3. Think aboutthe relating graph, Y is equal toX plus 1 squared minus 3. Andthink about what each component does.

The minus 3 moves the graph down three.So that is taking the Y value down three.If we are dealing with the X equals,it's going to do the same thing.Instead of taking the Y down 3 it takesthe X down 3. So what you're doingis making the X three units smaller.So we would take our vertex and moveit back 3. Similarly to the X plus 1.

What this is going to do is move our Xcoordinate of our vertex back one fora vertical parabola.It's going to move the Y back oneon a side-to-side parabola.By taking the Y back one what that meansis making the Y one smaller or movingit down one.

We don't have any coefficients to makethis any steeper or wider, so what wefound out is that our vertex is backthree, one, two, three and down one.Our coefficient is positive, which tellsus we have in this case an upward facingparabola where our Y values aregoing to be getting bigger.

Here we have no coefficient which then tellsus the opposite, our X coordinatesare going to be getting bigger.We're dealing with negative Xs andit's going to be going this way.We're going to have something like this.Again, you could always plug in a pointif you want to get a little bit moreprecise graph.

Here we're dealing with negative one.So I would probably end up plugging inY equals 0 to get an extra point.But what we've done is basically grapheda horizontal parabola by finding thevertex, pretty much the exact same wayas we did before but just switchingour X and our Ys.

Just to note, again this is not a function.The two pieces together, we could breakit up and look at either just the topor just the bottom and those are functions.But together when we're dealing with anentire sideways parabola, it's not afunction.